GL(3,𝔽₂)⋊C₄ #10621461

order	672
isoclinism	isoclinic class of SO(3,𝔽₇)
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₂

Aliases

	subgroup	G/H
center, Frattini, Fitting, hypercenter	C₂	SO(3,𝔽₇)
commutator, hypocenter	GL(3,𝔽₂)	C₄
socle, prime radical, cosocle	C₂×GL(3,𝔽₂)	C₂
LCS	G ▷ GL(3,𝔽₂)
UCS	C₁ ◁ C₂

43 conjugacy classes of subgroups.

minimal degree	μ(G) = 12
transitive degree	μ_t(G) = 28

A minimal faithful permutation representation — 2 generators on 12 points:

(1,8,2,5,7,4,6,3)(9,11,10,12);(1,6,3)(4,8,5)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(672, 1043);